Brushless reluctance-motor drivesThe variable-reluctance or switched-reluctance motor hassome remarkable characteristics that make it attractive fordozens of applications. With CAD software now available, andmany prototypes established, there should be few technicalbarriers between the laboratory and a number of successfulniches in the drives market

by Tim Miller

Reluctance motors have a history of not quiteachieving the power density, efficiency orpower factor of other established motors suchas the induction motor and the various formsof permanent-magnet (PM) motor. But recentadvances in electromagnetic design and powerelectronics have resulted in much improvedreluctance motors, with a wider range ofpossible characteristics; and the ever-increasingvariety and volume of the adjustable-speeddrives market is creating opportunities forwhich the modern reluctance motor is verycompetitive.1

This article is mostly about the switched-reluctance (SR) motor and its control, andpresents a few new ideas along with a reviewof some of the well known ones. Thesynchronous reluctance motor is also discussedas a potentially useful technology forapplications where the advantages of thereluctance motor are needed, but where verylow torque ripple, or compatibility with ACcontrol techniques, is or are required. Most ofthe article is relevant to drives in the rangefrom a few watts up to perhaps 50 kW.

Among the advantages of the reluctancemotor are the simple construction and theabsence of permanent magnets, whicheliminates cost in both raw material andmanufacturing processes (see Fig. 1). Theabsence of rotor windings and low rotor losseshelp to make the machine robust and suitablefor high-speed and high-temperatureapplications; or in other environments wherebrushless PM motors could be hazardousbecause of their open-circuit voltage or short-circuit current. Under almost all electrical faultconditions the reluctance motor is inert andcompletely safe, and it can fairly be describedas fault tolerant; the same is true for mostinverter faults, and indeed certain of theinverter faults that plague AC drives are notpossible with SR drives.

On the negative side, the SR motor tends tohave more torque ripple and a higher noiselevel than other motors. The reputation fornoise is almost certainly derived from earlymodels, since quiet SR motors have beendeveloped more recently (early inductionmotors had the same development problem).

The torque ripple, which can be in the range10-30%, is indeed a concern; but this hassometimes been used against the SR motorwithout regard to the torque ripple producedby induction motors or PM brushless motors,which can be just as bad. Many applicationsare not sensitive to torque ripple even of thismagnitude; for those that are, the SR driveshould be evaluated with caution, and ifreluctance-motor properties are needed, thesynchronous version should be considered asan alternative.

It is also true that the SR motor cannot becontrolled from a conventional AC inverter.However, to some this is an advantage,because the SR controller is arguably simplerand requires less protection. But the kVArequirement is typically higher than for ACdrives: anywhere from 0 to 30% higher in smallintegral-horsepower sizes. Depending on thetorque/speed characteristics required, and theduty cycie, this does not necessarily imply thatthe AC drive always has the advantage. Over awide speed range the SR motor may have theadvantage.

The SR motor cannot start or run from analternating-voltage source, and it is notnormally possible to operate more than onemotor from one inverter.

The interest in reluctance motors is muchincreased today compared with only five yearsago, and there are now innumerabledevelopment groups working on it worldwide.But because the design is difficult, particularlyin dealing with the magnetic circuit and thecalculation of losses, it is likely that manydisappointing models will yet be built beforethe technology is mature enough to begenerally viable. Meanwhile, it can be expectedthat the successes will steadily establish usefulniches in the drives market where the specialcharacteristics fit the requirements at the rightprice.

Torque capabilityBecause the SR motor is fundamentally a

step motor, it produces torque in impulses.During one step the phase current and thecorresponding flux linkage follow a closedtrajectory as shown in Fig. 2. The trajectory lies

POWER ENGINEERING JOURNAL NOVEMBER 1987 325

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The energy W converted from electrical tomechanical during one step is equal to thearea enclosed by the trajectory in Fig. 2. Theaverage electromagnetic torque T is then givenby

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where qNri the number of steps per revolution,is given by the product of the phase number qand the rotor pole number3 Nr. Clearly it isdesirable to design the motor to maximise theavailable conversion area between theunaligned and the aligned curves in order toget the most torque per ampere of phasecurrent. This requires a large alignedinductance, a small unaligned inductance, anda high saturation flux linkage. While thegeometry is simple, it is by no means easy toachieve these objectives in design calculations,and computer methods are essential to get agood result.2 For very detailed design work thefinite-element method is helpful, but simplermethods suffice in many cases.

In Fig. 2 only a small fraction of the availableenergy is converted. This is typical of smallmotors where the current is thermally limited.An increase in scale naturally permits more ofthe available energy to be converted. The sameincrease could be obtained with more intensecooling, or alternatively during intermittentoperation. However, operation with an extremetrajectory (such as the dotted curve in Fig. 2)may be inefficient and noisy, with a poorpower factor and peaky currents.

A rough estimate of the maximumattainable torque per unit rotor volume can bederived from an idealised triangular areaapproximating to the dotted trajectory inFig. 2. Following the methods of Reference 4,the result is

P9 n e w t o n metres/ m3R

1 (a) Schematic cross-section of 1 5 kW switched-reluctance motor with twoopposite poles of one phase excited; (b) partially wound SR motor stator; [c) rotorof SR motor

where Bs is the flux density in the stator polesat the maximum flux linkage tps in the alignedposition; A is the aligned/unalignedunsaturated inductance ratio; /8 is the pole arc(assumed equal for stator and rotor); and g isthe airgap. For a three-phase motor with sixstator and four rotor poles having a pole arc of30° and an air gap of 0-25 mm, at a rotorradius R of 25 mm, it should be possible toachieve ^ = 10 and Bs = ? -6T, giving a specifictorque of 60kNm/m3 from the extremetrajectory. With the small trajectory in Fig. 2the specific torque will be closer to15kNm/m3, and this figure is definitely

326 POWER ENGINEERING JOURNAL NOVEMBER 1987

competitive with induction and PM brushlessmotors.5

This simple analysis does not confirm thatsuch values can be obtained with acceptablelosses, efficiency and power factor; for this,much more calculation is necessary.2 Forexample, the simple torque formula indicatesan increase of torque with air gap g, but thiscan be sustained only if the inductance ratiocan be maintained constant and the same flux-density levels can be reached withoutoverheating the windings. The simple formulagives no guidance on these questions.However, it can be said that sufficient SRmotors have been built and tested, by manyindependent engineering groups, to confirmthat the values quoted are practicable and canbe obtained with high efficiency and quietoperation.

The balance of copper and iron losses isdifferent from that found in AC and PMbrushless motors. In the SR motor the flux-density waveform is very nonsinusoidal anddiffers from one part of the magnetic circuit toanother. The largest component of iron loss isoften in the stator yoke, simply because thissection has the greatest volume. Here thedominant frequency is equal to the step rate,especially at low speeds when the current islimited by PWM of the voltage. For motorswith the same number of rotor poles, the steprate of the SR motor exceeds the frequency ofthe AC (or PM brushless) motor by the factor2q; i.e. by 6 times in a three-phase motor.However, the hysteresis losses tend to bereduced by a factor of perhaps 2 -or 3, by theunipolar nature of the flux pulsations in mostsections of the core. Moreover, the peak fluxdensity is generally lower than in AC motorsbecause of the need to avoid couplingbetween the phases. These factors bring theiron losses more into line with those of ACmotors, and indeed they may be relativelylower because the SR motor has significantlyless iron than an AC motor of the same framesize.

At all but the highest speeds the copperlosses are usually more significant, particularlyin small motors6 (below, say, 5kW). To minimisethese, a large slot is desirable, which results inan optimum rotor diameter which tends to bea little smaller than the corresponding one forAC or PM brushless motors. Together with theheavily notched shape of the rotor, this usuallyleads to a very low inertia.

It is impossible to generalise about therelative efficiencies of SR and other types ofmotor without specifying very tightly theparameters that are kept the same in thecomparison. For the same frame size the SRmotor should be expected to have a lowerefficiency than that of the best PM motors, butbetter than that of a standard induction motor.(It must be added that non-standard inductionmotors, relieved of the line-start requirement,can be significantly more efficient thanstandard motors.) However, if the motor cost is

2 Locus of operating pointin the current/flux-linkageplane, showing theenergy W converted ineach step

3 (a) Phase-currentwaveform obtained withcurrent-regulated PWM.(b) Phase-currentwaveform obtained withfixed-frequency voltagePWM; the choppingfrequency is much higherthan in (a)

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kept the same, the SR motor should be themost competitive, because it requires fewermanufacturing processes and should have lessraw material for the same torque. In 'larger*sizes (say, above 10-20kW), the inductionmotor improves rapidly while the magnet costputs the PM motor out of contention.Efficiency differences then become marginal,and other factors will determine the choice.

ControlFor motoring operation the pulses of phase

current must coincide with a period of positiverate of change of inductance, i.e. when a pairof rotor poles is approaching alignment withthe stator poles of the excited phase. Thetiming and dwell of the current pulse are bothimportant in determining the efficiency, thetorque per ampere, the smoothness ofoperation, and other parameters. It is

characteristic of good operating conditionsthat the trajectory of Fig. 2 fits snugly in thespace between the unaligned and alignedmagnetisation curves.

The trajectory of Fig. 2 corresponds to high-speed operation where the current is limited bythe self-EMF of the phase winding. A smoothcurrent waveform is obtained with a peak/RMSratio very close to that of a half sine wave. Thiswaveform is not stressful to the powersemiconductors; indeed the duty cycle is higherthan that of a comparable AC or PM brushlessmotor controller, which should benefit thereliability.

At low speeds the self-EMF of the winding issmall and the current must be limited bychopping or pulse-width modulation (PWM) ofthe applied voltage. The strategy employed hasa profound effect on the operatingcharacteristics. Fig. 3a shows a currentwaveform controlled by a current regulatorthat maintains a more or less constant currentthroughout the conduction period in eachphase. The chopping frequency varies becauseof the changing motor inductance. Fig. 4ashows the corresponding flux-linkage/currenttrajectory, and Fig. 5a shows schematically themethod of control. As the current referenceincreases, the torque increases roughly linearly.This type of control produces a constant-torque type of characteristic as indicated inFig. 6a. To obtain speed control, a speedfeedback loop is necessary. This requires aspeed sensor in addition to (or integral with)the shaft-position sensor that is alreadyassumed to be present for providing the x

commutation signals. It can be noted that thisform of current regulation requires currenttransducers of wide bandwidth, in series withthe windings. Most of the published literatureon SR drives describes this form of control.

Fig. 3b shows, for the same motor, thecurrent waveform obtained with fixed-frequency PWM of the voltage. This can beimplemented with one of the transistors ineach phase leg; or alternatively as describedbelow. The corresponding energy-conversiontrajectory is shown in Fig. 4b, and the controlschematic in Fig. 5b. The duty cycle (or 'offtime') of the PWM can be varied by a simplemonostable circuit. What is found is that themotor now has a constant-speed characteristicas shown in Fig. 6b. This is not so surprising ifit is realised that this form of control isessentially similar to armature-voltage controlin a DC motor. Note that a controlled constant-speed characteristic is now obtained withoutthe expense of current sensors or a speedtransducer.

A simple form of current feedback can beadded to the circuit of Fig. 6b with interestingbenefits. A single inexpensive resistor in thereturn DC line provides a signal that, suitablyfiltered, can modulate the duty cycle of thePWM in such a way as to 'compound' thetorque/speed characteristic; it is possible in thisway to achieve under-compounding, over-compounding, or flat compounding, just as in aDC motor with a wound field. For manyapplications the speed regulation obtained by

328 POWER ENGINEERING JOURNAL NOVEMBER 1987

this simple scheme will be perfectly adequate.For precision speed control, of course, a normalspeed feedback loop can be added. The singlecurrent sensor also serves for thermal-overcurrent sensing.

A further remarkable feature of the voltagePWM scheme is that the current waveformtends to retain much the same shape over theentire operating range of speed and torque.This permits a high degree of utilisation of theavailable conversion energy over the wholerange, ensuring high overall efficiency andpower factor.

When the PWM duty cycle reaches 100%,the motor speed can be increased byincreasing the dwell (the conduction period) orthe advance of the current pulse relative to therotor position, or both. These increaseseventually reach maximum practical values,after which the torque becomes inverselyproportional to speed-squared. The speedrange over which constant power can bemaintained is comparable to that for inductionmotors, and is markedly better than for PMbrushless motors.

It is interesting to compare the twoalternative control schemes for the SR motorwith the one normally used for PM brushlessmotors. In the PM motor the flux is fixed bythe magnet. Fixed-frequency PWM (with avariable duty cycle) results in a constant-torquecharacteristic, so that speed feedback isnecessary for speed control in manyapplications.

Shaft-position sensingThe commutation requirement of the SR

motor is very similar to that of a PM brushlessmotor; it is even possible to use the sameshaft-position sensor and, in some cases, thesame integrated circuit to decode the signalstherefrom and control the PWM. (Several suchICs are now commercially available.) Much hasbeen made of the undesirability of the shaftsensor, because of the associated cost andspace requirement, and because there is anadded source of potential failures. However,the sensing requirement is no greater and noless than that of the PM brushless motor, andreliable methods are well established.

Operation without the shaft sensor ispossible and several schemes have beenreported.7 But to achieve the performance

possible with even a simple shaft sensor (suchas a slotted disc or a Hall-effect device),considerable extra complexity is necessary inthe controller, particularly if good starting andrunning performance is to be achieved with awide range of load torques and inertias. Forrapid acceleration and/or deceleration cycles,or for position control, there is a long way togo before the sensor can be eliminated.Probably the same is true of the PM brushlessmotor, and even the induction motor is notwithout its problems in this area.

Controller circuitsThe torque is independent of the direction

of the phase current, which can therefore beunidirectional. This permits the use of unipolarcontroller circuits, with a number ofadvantages over the corresponding circuits forAC or PM brushless motors, which requirealternating current.

Fig. 7 shows a circuit well suited for use withtransistors (bipolar, field effect, or insulatedgate). The phases are independent, and in this

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6 (a) Speed/torquecharacteristic obtainedwith current regulation.(b) Speed/torque curveobtained with voltagePWM; the dotted curveshows the effect ofreduced current-feedbackgain ('under-compounding')

POWER ENGINEERING JOURNAL NOVEMBER 1987 329

7 Controller circuit for SRmotors, suitable for usewith transistors

8 Controller circuit withonly four transistors andfour diodes for a three-phase SR motor. Thecircuit has nearly thesame function as Fig. 7,but only operates in thePWM mode and cannotadmit overlap betweenphases. Bottom transistorsare used for commutationonly (Patent applied for)

respect the SR controller differs from the ACinverter, in which the motor windings areconnected between the midpoints of adjacentinverter phase legs. The winding is in serieswith both switches, providing valuableprotection against faults. In the AC inverter theupper and lower phase-leg switches must beprevented from switching on simultaneouslyand short-circuiting the DC supply; this ispossible only by means of additional controlcircuitry, which is unnecessary in the SRcontroller.

The upper and lower phase-leg switchesmay be switched on and off together, but abetter mode of operation is to use one forcommutation and the other for PWM. At thestart of the conduction period both switchesare turned on. One remains on during thewhole conduction period, while the other is'chopped' by a control strategy such as thosedescribed in the previous Section. At the endof the conduction period both switches areturned off and any remaining stored magneticenergy that is not converted to mechanicalwork is returned to the supply by the currentfreewheeling through the diodes. At highspeeds, if the PWM regulator 'saturates', bothswitches will be turned on and off together.

The inductance level of the SR motor, whileit varies with the rotor position, is generallyhigher than in PM brushless motors. For thesame chopping frequency the ripple current istherefore smaller. This helps to ensure quietoperation, especially if the chopping frequencyis high. Chopping frequencies of 10-20 kHz areare desirable, as in other types of drive, tominimise acoustic noise. In large drives (say,above 20 kW) it becomes much more difficultto chop at such a high frequency because ofthe switching-speed limitations and losses oflarger devices (such as GTOs). This makes it

more difficult to achieve quiet operation inlarger motors, particularly at low speeds.

In small drives it is often acceptable to usePWM control over the entire speed range. Thisis the normal approach with surface-magnetPM brushless motors. In such cases the SRcontroller circuit can profitably be reduced tothe circuit of Fig. 8, in which the chopping isperformed by one transistor in common for allthe phases. The lower transistors commutatethe chopped voltage to the phases in propersequence, under the control of the shaft-position sensor. The circuit requires only n+1transistors and n+1 diodes for a motor with nphases. A three-phase motor thus requires onlyfour transistors and four diodes. There ispractically no loss of functionality with thiscircuit relative to the full circuit having 2ntransistors in Fig. 7. Its main limitation is thatthere can be essentially no overlap betweenthe conduction periods of adjacent phases; butthis limitation only becomes a problem at verylow (crawling) speeds and possibly at very highspeeds. Otherwise the circuit has only two-thirds of the power devices of a brushless PMmotor controller, and it is simpler to control.

Many other circuits have been developed inattempts to reduce the number of switches allthe way down to n, and to take full advantageof the unipolar operation of the SR motor. Butit seems that in every case there is a penalty inthe form of extra passive components orcontrol limitations.8

New developments

Solid rotorsIn the conventional SR motor both rotor and

stator are laminated; induced currents in eithermember would generally impair the torqueproduction and produce additional losses. Ifthere were no magnetic saturation theinstantaneous torque could be expressed as

2 dd

where / is the phase current; L is the phaseinductance; and 6 is the rotor angular position.If now the rotor is made solid, or if short-circuited conducting loops are affixed to thepoles, then the torque is given by the sameexpression, but with L replaced by

11 = L (1 - tf)

where k is the coupling coefficient betweenthe stator winding and the rotor circuit. L' isthe leakage inductance and is completelydefined by this equation. It is, of course,meaningful only when the stator flux ischanging at a sufficiently rapid rate to ensurethat the induced currents in the rotor are'inductance limited'; this, however, is notdifficult to achieve. Fig. 9 shows anexperimental rotor of this type.

With suitable pole geometry the minimumvalue of 11 occurs when the stator and rotorpoles are aligned, and the maximum value iswhen they are unaligned. Should it be possibleto achieve a higher inductance ratio betweenthese two extreme positions than with the

330 POWER ENGINEERING JOURNAL NOVEMBER 1987

conventional laminated rotor, this machinewould be able to achieve a higher torque perampere. Even without this advantage, the solidrotor has intriguing possibilities for very highspeeds because its lateral stiffness is inevitablygreater than that of the normal laminatedrotor. Rotor losses may seriously limit theviability of this concept, which has yet to bedeveloped beyond a laboratory machine.However, the possibilities for liquid cooling aremuch better in a solid rotor than in alaminated one. Interestingly, the current pulsesmust now be phased to coincide with theseparation of the poles, and not with theirapproach. The torque is produced by repulsion,not by attraction.

Synchronous-reluctance motorsThe synchronous-reluctance motor is well

known in its line-start version. Both the rotorand the stator present cylindrical surfaces tothe air gap. The stator is a conventionalpolyphase AC stator, while the rotor hasinternal flux barriers shaped to minimise theratio of d-axis to q-axis reactance. The rotorhas a starting cage to provide across-the-linestarting, and operation is normally from avoltage source in an open-loop mode (withoutshaft-position feedback). It is necessary tooperate at a safe fraction of the pull-outtorque, and this requirement, together with theneed to design for stable operation over a widespeed range, constrains the design in such away that both power factor and efficiency arepoor by comparison with modern AC or PMbrushless drives.

At the same time the switched reluctancemotor has a certain torque ripple, and it wouldbe beneficial to eliminate this by converting toa synchronous-reluctance motor with a PWMsine-wave inverter. The question remains as towhether the synchronous motor could equalthe efficiency, power density and power factorof the switched motor; and how would theyboth compare with induction and PM motors?It is difficult to answer this question in general.But for certain application requirements it maybe that the cageless synchronous reluctancemotor, fed with current-controlled PWM sinewaves oriented to the rotor position, anddesigned without the stability constraints ofthe line-start motor, can achieve competitiveperformance levels. This suggests aninteresting candidate for applications with veryhigh ambient temperatures, or others wherepermanent magnets are undesirable for safetyor reliability reasons. There is evidently plentyof fundamental research still to be done.

ConclusionFor applications requiring high-temperature

operation or a high degree of fault tolerance,or in cases where a brushless motor is neededbut without the cost or the operationalproblems of permanent-magnet motors,switched- and synchronous-reluctance motorsare viable candidates. With CAD to optimisethe motor and predict performance, and withthe exploitation of modern power-electronicsand control techniques, these drives can be

expected to find several applications in theever-expanding market for adjustable-speedmotor drives.

AcknowledgmentsThe author would like to acknowledge many

colleagues in UK and US industry anduniversities, particularly the co-authorsmentioned in the references. P G. Bower ofGlasgow University has helped considerably inthe development of the control techniques,Alan Hutton wi th motor design, and MalcolmMcGilp w i th design software.Acknowledgment is also due to the Science &Engineering Research Council for a grant tostudy the cageless synchronous-reluctancemotor; to General Electric (USA); and to thesubscribing companies of the GlasgowUniversity SPEED programme.

References1 MILLER, T. J. E.: 'Small motor drives expand their

technology horizons', Power Engng. J. 1987,1,pp. 283-289

2 MILLER, T. J. E.: 'PC CAD for switched reluctancedrives', IEE Conference on Electric Machines andDrives, London, 16th-18th November, 1987

3 MILLER, T J. E.: 'Converter volt-ampererequirements of the switched reluctance drive',IEEE Trans., 1985, IA-21, pp. 1136-1144

4 HARRIS, M. R.: 'Static torque production insaturated doubly-salient machines', Proc. IEE,1975,122, (10), pp. 1121-1127

5 HARRIS, M. R., FINCH, J. W, MALLICK, J. A , andMILLER, T. J. E.: A review of the integral-horsepower switched reluctance drive', IEEETrans., 1986, IA-22, pp. 716-721

6 JAHNS, T. M., and MILLER, T. J. E.: A current-controlled switched reluctance drive for FHPapplications', Conference on Applied MotionControl, Minneapolis, USA 10th-12th June,1986

7 BASS, J. T, EHSANI, M., and MILLER, T. J. E.:'Simplified electronics for torque control ofsensorless switched reluctance motor' IEEETrans., 1987, IE-34, pp. 234-239

8 BASS, J. T, EHSANI, M., MILLER, J. J. E., andSTEIGERWALD, R.: 'Development of a unipolarconverter for variable-reluctance motor drives',IEEE Trans, 1987, IA-23, pp. 545-553

© IEE: 1987

Tim Miller is Titular Professor in Power Electronics,The University, Glasgow G12 8QQ, UK. He is an IEEMember

9 Rotor of solid-rotor SRmotor with conductingloops to provide reducedsecondary resistance; theideal loop resistance iszero. This motor would bean interesting way toexploit room-temperaturesuperconductors if theyever become availablewith sufficient current-density capability

POWER ENGINEERING JOURNAL NOVEMBER 1987 331

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332 POWER ENGINEERING JOURNAL NOVEMBER 1987